ITLS6002 Chap.3 Advanced Inventory Decisions
Advanced Inventory Decisions
Advanced inventory planning selects a policy that matches the structure of the decision rather than forcing every case into EOQ. Quantity discounts require total landed-cost comparisons across feasible price ranges. Single-period products use an underage-versus-overage trade-off. Time-varying demand calls for lot-sizing or mixed-integer models that connect periods through inventory balance.
Multi-echelon systems add a second location question: where stock is physically held and where it should count for control. This chapter provides a model-selection routine, boundary checks and interpretation rules for comparing solutions that may be mathematically close but operationally different.
A discount solution tests a feasible EOQ or the lower breakpoint for every price bracket and includes purchase cost in the comparison. A newsvendor answer builds underage and overage costs from the case before taking the corresponding demand percentile. Dynamic lot sizing preserves product flow across time, while a binary setup variable links a fixed ordering cost to positive quantity.
Echelon analysis prevents upstream and downstream stock from being treated as unrelated buffers when they protect the same demand stream.
What this chapter covers
- 01
Quantity-discount candidate testing
- 02
Single-period newsvendor logic
- 03
Time-varying lot sizing
- 04
Mixed-integer inventory models
- 05
Echelon versus installation stock
- 06
Model selection and boundary checks
Worked example · free
Choosing a quantity-discount order
- 2At $20, EOQ is sqrt(2 x 5,000 x 80 / 4) = 447.21 units, which is feasible in the first bracket.
- 2At $19, EOQ is sqrt(2 x 5,000 x 80 / 3.8) = 458.83 units, which is infeasible, so test the 1,000-unit break.
- 2Total annual cost at 447 units is about 100,000 + 894.4 + 894 = $101,788.4.
- 2Total annual cost at 1,000 units is 95,000 + 400 + 1,900 = $97,300.
Key terms
- Critical Fractile
- The target demand percentile implied by relative underage and overage costs.
- Underage Cost
- The marginal consequence of ordering one unit too little in a single-period setting.
- Echelon Stock
- Inventory at one stage plus inventory downstream that it supports.
- Setup Variable
- A binary model variable indicating whether ordering or production occurs in a period.
Advanced Inventory Decisions FAQ
Why must quantity-discount breakpoints be tested?
An EOQ computed using a lower price may fall outside that price bracket. The breakpoint is the smallest feasible quantity receiving the discount, and its lower purchase cost can dominate even when it raises cycle-stock holding cost.
When is a newsvendor model inappropriate?
It is inappropriate when unsold stock carries normally into repeated replenishment cycles or when shortages are routinely backordered. The model is intended for a single selling opportunity with clearly defined overage and underage consequences.
What does a binary setup variable add to a lot-sizing model?
It connects a fixed setup cost to the decision to order or produce. A linking constraint prevents positive quantity unless the setup variable is activated, allowing the optimiser to trade larger batches against inventory carrying cost.
Which costs belong in an all-units discount comparison?
Compare annual purchase, ordering and holding costs for every feasible candidate. Holding cost changes when it is calculated as a proportion of price, and purchase cost must be included because the unit price differs across brackets. Reject any candidate that does not qualify for its assumed price.
How is the newsvendor critical fractile interpreted?
It is the cumulative demand probability where the marginal cost of ordering too little balances the combined overage and underage consequences. The resulting quantity is a percentile, not an expected demand plus an arbitrary safety percentage, so define both costs before consulting the distribution.
What is the difference between installation stock and echelon stock?
Installation stock concerns one location's own inventory. Echelon stock includes that location plus downstream inventory it supports. The distinction matters because an upstream policy based only on local stock can ignore protection already present elsewhere in the network.
Exam move
Build a short decision tree keyed to price breaks, product life, time-varying demand and network level. For discounts, calculate a candidate in every bracket and compare full annual cost. For single-period questions, define underage and overage costs in words before taking a percentile. For dynamic models, write the inventory-balance row for one period and explain every variable before expanding it across the horizon.
Practise identifying the model from a short business description before calculating anything. In a discount problem, mark every bracket as feasible or infeasible and keep a candidate-cost table. In a newsvendor problem, test whether changing salvage value moves the critical fractile in the expected direction.
For multi-period planning, reconcile opening stock, orders, demand and closing stock on every row, then verify the horizon total. In echelon cases, sketch the network and circle the downstream inventory counted by each control point before assigning parameters.
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